The invention relates to a method for the temporal interpolation of images enabling the reconstitution of the luminance values of the pixels of a missing image in a series of images representing the same object. Such a method is used, for example, for a transmission of video images at a very low rate, consisting in transmitting only certain frames, with a coding reducing the data rate, and in restoring the frames not transmitted by interpolation from the transmitted and decoded frames. It can also be used for the conversion of a series of video images using a standard having a frequency of 50 Hz to a standard having a frequency of 60 Hz, or vice-versa. For such a conversion, most of the frames must be interpolated from frames available at the frequency of 50 Hz, as the instants of shooting at the frequency of 60 Hz do not coincide with the instants of shooting at the frequency of 50 Hz.
The object of the interpolation is therefore to determine a luminance value L(IX,IY,T.sub.j) for each pixel of a frame to be interpolated corresponding to an instant T.sub.j from the luminance values L(IX,IY,T.sub.a) and L(IX,IY,T.sub.b) of the pixels of two known frames corresponding to instants T.sub.a and T.sub.b such that T.sub.j occurs between T.sub.a and T.sub.b. The pixels of the frames are referenced by the coordinates (IX,IY) of their centers in an ortho-normed reference system which is common to all the frames.
A first category of temporal interpolation methods is based on a simple linear interpolation consisting in computing, for each pixel to be interpolated, a linear combination of two luminance values of pixels having homologous coordinates (IX,IY) in the two known frames corresponding to the instants T.sub.a and T.sub.b, weighted by the durations T.sub.b -T.sub.j and T.sub.j -T.sub.a, according to the formula: ##EQU1##
The homologous coordinates are exactly identical if 5 the two frames T.sub.a and T.sub.b have the same parity and are identical to within half a line if they have different parities.
This category of methods enables a good restitution of fixed zones in a series of frames as in this case the luminance values used for the interpolation actually correspond to a same point of the object represented by the series of frames. On the other hand, zones in motion are poorly restored and become more blurred as the speed of motion increases.
A second category of methods takes account of the motion of the object represented by the two known frames. These methods consist in assuming that each point of an object in motion represented by the series of frames displaces from the first known frame to the second known frame by means of an elementary translation at constant velocity. Known methods enable the determination of a velocity vector V=(VX,VY) for each pixel of the frame to be interpolated. This vector represents an elementary translation of the pixel, which does not necessarily correspond to the velocity of the represented object but corresponds to the variations in the luminance of the pixels representing that object.
These methods of the second category then consist in computing an interpolated value of luminance for each pixel, taking account of two displacements in opposite senses respectively in the two known frames. These two displacements are in the direction of the velocity vector associated with the pixel to be interpolated and respectively have a modulus proportional to the time interval separating the frame to be interpolated and the known frame concerned. Each interpolated luminance value is therefore computed according to the formula: ##EQU2##
This category of methods enables a more precise restitution of the zones in motion as well as of the fixed zones of the frames to be interpolated. But the implementation of this category of methods includes a major difficulty which is the determination of a velocity vector to be associated with each pixel to be interpolated. A first known method, described by H. C. Bergman in "Motion Adaptive Frame Interpolation 1984 International Zurich Seminar on Digital Communications", consists in associating with each pixel to be interpolated the estimated velocity vector for the pixel having the same coordinates in the first known frame. This association is always more or less inaccurate since in the zones in motion these two pixels do not represent a same point of the object in motion. This association is only exact insofar as adjacent points of the object in motion have the same velocity vector, which is not necessarily the case, particularly if the represented object is undergoing a rotation. The fidelity of restitution of images therefore varies, in the zones in motion, depending on the type of motion in these zones.
A second known method, described by M. Bierling and R Thoma in "Motion compensating field interpolation using a hierarchically structured displacement estimator" consists in estimating a velocity vector for each pixel of each frame to be interpolated, independently for each frame to be interpolated. This estimation is made from the same pair of known images, for all the frames to be interpolated corresponding to instants between T.sub.a and T.sub.b, but it takes account of the duration of the time intervals separating the frame to be interpolated and the known images and, consequently, the velocity vector associated with each pixel to be interpolated has a much more accurate value than that associated by means of the previously described method. The fidelity of restitution of the frames in the zones in motion is therefore made independent of the type of motion. On the other hand, this second method has the disadvantage of multiplying the computing time necessary for the estimation of the velocity vectors, since it is proportional to the number of frames to be interpolated between the two known frames.